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If employees can have intervals with negative start or end times (e.g., [-5, 0]) or zero-length intervals, which modification to the sweep line algorithm is necessary to correctly find free time?

hard🎤 Interviewer Follow-up Q15 of Q15
Intervals - Employee Free Time
If employees can have intervals with negative start or end times (e.g., [-5, 0]) or zero-length intervals, which modification to the sweep line algorithm is necessary to correctly find free time?
AIgnore zero-length intervals and ensure sorting places end events before start events at ties
BTreat zero-length intervals as free time intervals
CSort events only by time, ignoring event type
DMerge touching intervals as free time gaps
Step-by-Step Solution
  1. Step 1: Handle zero-length intervals

    Zero-length intervals like [2,2] do not represent busy time and should be ignored to avoid false free intervals.
  2. Step 2: Maintain correct sorting order

    Sorting end events before start events at same time prevents reporting free time between touching intervals or zero-length intervals.
  3. Final Answer:

    Option A -> Option A
  4. Quick Check:

    Ignoring zero-length intervals and correct sorting avoids invalid free times [OK]
Quick Trick: Ignore zero-length intervals and sort end before start events [OK]
Common Mistakes:
MISTAKES
  • Counting zero-length intervals as free time
  • Sorting start before end events
Trap Explanation:
PITFALL
  • Naive sorting or including zero-length intervals causes incorrect free time detection.
Interviewer Note:
CONTEXT
  • Tests candidate's ability to adapt algorithm to relaxed constraints and edge cases.
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